### Wednesday, March 05, 2008

## JSH: Cutting edge research, your reaction

I've focused on an incredibly simple result that reaches to the limits of what the modern mathematical world knows about factoring as it covers the difference of squares, as if T mod 3 = 2, and

z^2 = y^2 + T

then

z = (1 + 2a^2)k/(2a)

for some integers k and 'a'.

Now the T mod 3 = 2 means that trivially the equation is always satisfied when a=1 and k is even, but there are plenty of examples that you can find where 'a' is greater than 1 and z dutifully has 1+2a^2 as a factor, and no cases where it does not work.

So z will have 9 as a factor or 33, or 51 because there is this mathematical rule that I like to call the z constraint, which makes it so.

To make the result more like what most math people learn you can have

x^2 = y^2 + N

and

x = (1+2a^2)k/(2a)

and the same result.

It gets more fun though as if you play with z you will find that, if f_1*f_2 = T, and p is some odd prime that you pick where k exists such that

k^2 = (1 + a^2)^{-1}(T) mod p then, you get your factors mod p:

f_1 = ak mod p

and

f_2 = a^{-1}(1 + a^2)k mod p

as long as p is less than the smaller factor which I'll call f_1, or p - f_1 is less than f_1.

And you people fought my research because you thought you could get away with it.

Stupid.

You destroyed a math journal and kept that out of the news but later I can use that information to show that there had to be a conspiracy on multiple levels reaching all the way into the most prestigious institutions like the editorial board of Princeton University.

You tried to end human progress in mathematics and create a welfare system where mathematicians get paid to not only do nothing of value, but to try and destroy people who can.

And you kept at it as the drumbeats grew louder of a solution to the factoring problem, even though millions of people around the world could lose a LOT of money because you are con artists and con artists do not quit until the police are coming.

You always hang on for that last little bit before folding, which is what I expected as you never outsmarted me.

You just set yourselves up for easy convictions.

z^2 = y^2 + T

then

z = (1 + 2a^2)k/(2a)

for some integers k and 'a'.

Now the T mod 3 = 2 means that trivially the equation is always satisfied when a=1 and k is even, but there are plenty of examples that you can find where 'a' is greater than 1 and z dutifully has 1+2a^2 as a factor, and no cases where it does not work.

So z will have 9 as a factor or 33, or 51 because there is this mathematical rule that I like to call the z constraint, which makes it so.

To make the result more like what most math people learn you can have

x^2 = y^2 + N

and

x = (1+2a^2)k/(2a)

and the same result.

It gets more fun though as if you play with z you will find that, if f_1*f_2 = T, and p is some odd prime that you pick where k exists such that

k^2 = (1 + a^2)^{-1}(T) mod p then, you get your factors mod p:

f_1 = ak mod p

and

f_2 = a^{-1}(1 + a^2)k mod p

as long as p is less than the smaller factor which I'll call f_1, or p - f_1 is less than f_1.

And you people fought my research because you thought you could get away with it.

Stupid.

You destroyed a math journal and kept that out of the news but later I can use that information to show that there had to be a conspiracy on multiple levels reaching all the way into the most prestigious institutions like the editorial board of Princeton University.

You tried to end human progress in mathematics and create a welfare system where mathematicians get paid to not only do nothing of value, but to try and destroy people who can.

And you kept at it as the drumbeats grew louder of a solution to the factoring problem, even though millions of people around the world could lose a LOT of money because you are con artists and con artists do not quit until the police are coming.

You always hang on for that last little bit before folding, which is what I expected as you never outsmarted me.

You just set yourselves up for easy convictions.